Grade 8 - Patterns and Relations
Standard 8.PR.2 - Practice solving two step linear equations by combining like terms.
Included Skills: Algebra
Model and solve problems using linear equations of the form: • ax = b • x/a = b, a ≠ 0 • ax + b = c • x/a + b = c, a ≠ 0 • a (x + b) = c • concretely, pictorially, and symbolically, where a, b, and c are integers. • Identify and describe situations, which are relevant to self, family, or community, that can be modeled by a linear equation (e.g., the cost of purchasing x fish from a fisherman). • Model and solve linear equations using concrete materials (e.g., counters and integer tiles) and describe the process orally and symbolically. • Discuss the importance of the preservation of equality when solving equations. • Explain the meaning of and verify the solution of a given linear equation using a variety of methods, including concrete materials, diagrams, and substitution. • Generalize and apply symbolic strategies for solving linear equations. • Identify, explain, and correct errors in a given solution of a linear equation. • Demonstrate the application of the distributive property in the solving of linear equations (e.g., 2(x + 3); 2x + 6= 5) • Explain why some linear relations (e.g., x/a = b, a ≠ 0 and x/a + b = c, a ≠ 0) have a given restriction and provide an example of a situation in which such a restriction would be necessary. • Identify and solve problems that can be represented using linear equations and explain the meaning of the solution in the context of the problem. • Explain the algebra behind a particular algebra puzzle such as this puzzle written for 2008: - Pick the number of times a week that you would like to go out to eat (more than once but less than 10). - Multiply this number by 2 (just to be bold). - Add 5. - Multiply it by 50. - If you have already had your birthday this year add 1758. If you have not, add 1757. - Now subtract the four digit year that you were born. - You should have a three digit number. The first digit of this was your original number. The next two numbers are your age.